Unsupervised Learning: Trade&Ahead

Marks: 60

Context

The stock market has consistently proven to be a good place to invest in and save for the future. There are a lot of compelling reasons to invest in stocks. It can help in fighting inflation, create wealth, and also provides some tax benefits. Good steady returns on investments over a long period of time can also grow a lot more than seems possible. Also, thanks to the power of compound interest, the earlier one starts investing, the larger the corpus one can have for retirement. Overall, investing in stocks can help meet life's financial aspirations.

It is important to maintain a diversified portfolio when investing in stocks in order to maximise earnings under any market condition. Having a diversified portfolio tends to yield higher returns and face lower risk by tempering potential losses when the market is down. It is often easy to get lost in a sea of financial metrics to analyze while determining the worth of a stock, and doing the same for a multitude of stocks to identify the right picks for an individual can be a tedious task. By doing a cluster analysis, one can identify stocks that exhibit similar characteristics and ones which exhibit minimum correlation. This will help investors better analyze stocks across different market segments and help protect against risks that could make the portfolio vulnerable to losses.

Objective

Trade&Ahead is a financial consultancy firm who provide their customers with personalized investment strategies. They have hired you as a Data Scientist and provided you with data comprising stock price and some financial indicators for a few companies listed under the New York Stock Exchange. They have assigned you the tasks of analyzing the data, grouping the stocks based on the attributes provided, and sharing insights about the characteristics of each group.

Data Dictionary

• Ticker Symbol: An abbreviation used to uniquely identify publicly traded shares of a particular stock on a particular stock market
• Company: Name of the company
• GICS Sector: The specific economic sector assigned to a company by the Global Industry Classification Standard (GICS) that best defines its business operations
• GICS Sub Industry: The specific sub-industry group assigned to a company by the Global Industry Classification Standard (GICS) that best defines its business operations
• Current Price: Current stock price in dollars
• Price Change: Percentage change in the stock price in 13 weeks
• Volatility: Standard deviation of the stock price over the past 13 weeks
• ROE: A measure of financial performance calculated by dividing net income by shareholders' equity (shareholders' equity is equal to a company's assets minus its debt)
• Cash Ratio: The ratio of a company's total reserves of cash and cash equivalents to its total current liabilities
• Net Cash Flow: The difference between a company's cash inflows and outflows (in dollars)
• Net Income: Revenues minus expenses, interest, and taxes (in dollars)
• Earnings Per Share: Company's net profit divided by the number of common shares it has outstanding (in dollars)
• Estimated Shares Outstanding: Company's stock currently held by all its shareholders
• P/E Ratio: Ratio of the company's current stock price to the earnings per share
• P/B Ratio: Ratio of the company's stock price per share by its book value per share (book value of a company is the net difference between that company's total assets and total liabilities)

Importing necessary libraries and data

# Libraries to help with reading and manipulating data
import numpy as np
import pandas as pd

# Libraries to help with data visualization
import matplotlib.pyplot as plt
import seaborn as sns

sns.set_theme(style='darkgrid')

# Removes the limit for the number of displayed columns
pd.set_option("display.max_columns", None)
# Sets the limit for the number of displayed rows
pd.set_option("display.max_rows", 200)

# to scale the data using z-score
from sklearn.preprocessing import StandardScaler

# to compute distances
from scipy.spatial.distance import cdist, pdist

# to perform k-means clustering and compute silhouette scores
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score

# to visualize the elbow curve and silhouette scores
from yellowbrick.cluster import KElbowVisualizer, SilhouetteVisualizer

# to perform hierarchical clustering, compute cophenetic correlation, and create dendrograms
from sklearn.cluster import AgglomerativeClustering
from scipy.cluster.hierarchy import dendrogram, linkage, cophenet

# to suppress warnings
import warnings
warnings.filterwarnings("ignore")

# let colab access my google drive
from google.colab import drive
drive.mount('/gdrive')

Drive already mounted at /gdrive; to attempt to forcibly remount, call drive.mount("/gdrive", force_remount=True).

# Now we can import the data
data = pd.read_csv('/gdrive/MyDrive/MGL/T&A/stock_data.csv')

Data Overview

• Observations
• Sanity checks

# Let's first create a copy of the dataset to prevent unwanted changes
df = data.copy()

# Let's first check the shape of our data
df.shape

(340, 15)

# Now let's take a closer look at the first few rows of data
df.head(10)

	Ticker Symbol	Security	GICS Sector	GICS Sub Industry	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio
0	AAL	American Airlines Group	Industrials	Airlines	42.349998	9.999995	1.687151	135	51	-604000000	7610000000	11.39	6.681299e+08	3.718174	-8.784219
1	ABBV	AbbVie	Health Care	Pharmaceuticals	59.240002	8.339433	2.197887	130	77	51000000	5144000000	3.15	1.633016e+09	18.806350	-8.750068
2	ABT	Abbott Laboratories	Health Care	Health Care Equipment	44.910000	11.301121	1.273646	21	67	938000000	4423000000	2.94	1.504422e+09	15.275510	-0.394171
3	ADBE	Adobe Systems Inc	Information Technology	Application Software	93.940002	13.977195	1.357679	9	180	-240840000	629551000	1.26	4.996437e+08	74.555557	4.199651
4	ADI	Analog Devices, Inc.	Information Technology	Semiconductors	55.320000	-1.827858	1.701169	14	272	315120000	696878000	0.31	2.247994e+09	178.451613	1.059810
5	ADM	Archer-Daniels-Midland Co	Consumer Staples	Agricultural Products	36.680000	-12.017268	1.516493	10	49	-189000000	1849000000	2.99	6.183946e+08	12.267559	7.496831
6	ADS	Alliance Data Systems	Information Technology	Data Processing & Outsourced Services	276.570007	6.189286	1.116976	30	25	90885000	596541000	8.91	6.695185e+07	31.040405	129.064585
7	AEE	Ameren Corp	Utilities	MultiUtilities	43.230000	2.174424	1.124186	9	14	287000000	636000000	2.60	2.446154e+08	16.626923	-0.719497
8	AEP	American Electric Power	Utilities	Electric Utilities	58.270000	2.371753	1.068485	11	9	13900000	2052300000	3.13	4.218978e+08	18.456543	-3.022649
9	AFL	AFLAC Inc	Financials	Life & Health Insurance	59.900002	3.027181	1.048295	14	99	-308000000	2533000000	5.88	4.307823e+08	10.187075	-1.883912

# And now for a more detailed overview
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 340 entries, 0 to 339
Data columns (total 15 columns):
 #   Column                        Non-Null Count  Dtype  
---  ------                        --------------  -----  
 0   Ticker Symbol                 340 non-null    object 
 1   Security                      340 non-null    object 
 2   GICS Sector                   340 non-null    object 
 3   GICS Sub Industry             340 non-null    object 
 4   Current Price                 340 non-null    float64
 5   Price Change                  340 non-null    float64
 6   Volatility                    340 non-null    float64
 7   ROE                           340 non-null    int64  
 8   Cash Ratio                    340 non-null    int64  
 9   Net Cash Flow                 340 non-null    int64  
 10  Net Income                    340 non-null    int64  
 11  Earnings Per Share            340 non-null    float64
 12  Estimated Shares Outstanding  340 non-null    float64
 13  P/E Ratio                     340 non-null    float64
 14  P/B Ratio                     340 non-null    float64
dtypes: float64(7), int64(4), object(4)
memory usage: 40.0+ KB

df.describe()

	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio
count	340.000000	340.000000	340.000000	340.000000	340.000000	3.400000e+02	3.400000e+02	340.000000	3.400000e+02	340.000000	340.000000
mean	80.862345	4.078194	1.525976	39.597059	70.023529	5.553762e+07	1.494385e+09	2.776662	5.770283e+08	32.612563	-1.718249
std	98.055086	12.006338	0.591798	96.547538	90.421331	1.946365e+09	3.940150e+09	6.587779	8.458496e+08	44.348731	13.966912
min	4.500000	-47.129693	0.733163	1.000000	0.000000	-1.120800e+10	-2.352800e+10	-61.200000	2.767216e+07	2.935451	-76.119077
25%	38.555000	-0.939484	1.134878	9.750000	18.000000	-1.939065e+08	3.523012e+08	1.557500	1.588482e+08	15.044653	-4.352056
50%	59.705000	4.819505	1.385593	15.000000	47.000000	2.098000e+06	7.073360e+08	2.895000	3.096751e+08	20.819876	-1.067170
75%	92.880001	10.695493	1.695549	27.000000	99.000000	1.698108e+08	1.899000e+09	4.620000	5.731175e+08	31.764755	3.917066
max	1274.949951	55.051683	4.580042	917.000000	958.000000	2.076400e+10	2.444200e+10	50.090000	6.159292e+09	528.039074	129.064585

# Let's create a function to return the sum of unique values for each column in our data set
def count_unique_values(dataset):
    unique_counts = {}
    for column in dataset.columns:
        unique_counts[column] = len(dataset[column].unique())
    return unique_counts

# Now we can call our new function to print a list of the sum of unique values for each column
unique_values = count_unique_values(df)
unique_values

{'Ticker Symbol': 340,
 'Security': 340,
 'GICS Sector': 11,
 'GICS Sub Industry': 104,
 'Current Price': 336,
 'Price Change': 340,
 'Volatility': 340,
 'ROE': 82,
 'Cash Ratio': 124,
 'Net Cash Flow': 332,
 'Net Income': 335,
 'Earnings Per Share': 268,
 'Estimated Shares Outstanding': 323,
 'P/E Ratio': 295,
 'P/B Ratio': 299}

# Find duplicate values in specific columns
df.value_counts('GICS Sector')

GICS Sector
Industrials                    53
Financials                     49
Consumer Discretionary         40
Health Care                    40
Information Technology         33
Energy                         30
Real Estate                    27
Utilities                      24
Materials                      20
Consumer Staples               19
Telecommunications Services     5
dtype: int64

Insights

• To start, we appear to have all values of our data present.
• We have 4 object columns and 11 numerical columns.
• We have a total of 11 sectors represented and 104 sub industries represented.
• They Industrials sector is our most represented while Telecommunications is the least represented.

Exploratory Data Analysis (EDA)

• EDA is an important part of any project involving data.
• It is important to investigate and understand the data better before building a model with it.
• A few questions have been mentioned below which will help you approach the analysis in the right manner and generate insights from the data.
• A thorough analysis of the data, in addition to the questions mentioned below, should be done.

Questions:

1. What does the distribution of stock prices look like?
2. The stocks of which economic sector have seen the maximum price increase on average?
3. How are the different variables correlated with each other?
4. Cash ratio provides a measure of a company's ability to cover its short-term obligations using only cash and cash equivalents. How does the average cash ratio vary across economic sectors?
5. P/E ratios can help determine the relative value of a company's shares as they signify the amount of money an investor is willing to invest in a single share of a company per dollar of its earnings. How does the P/E ratio vary, on average, across economic sectors?

Function creation

# function to plot a boxplot and a histogram along the same scale.


def histogram_boxplot(df, feature, figsize=(12, 7), kde=False, bins=None):
    """
    Boxplot and histogram combined

    data: dataframe
    feature: dataframe column
    figsize: size of figure (default (12,7))
    kde: whether to the show density curve (default False)
    bins: number of bins for histogram (default None)
    """
    f2, (ax_box2, ax_hist2) = plt.subplots(
        nrows=2,  # Number of rows of the subplot grid= 2
        sharex=True,  # x-axis will be shared among all subplots
        gridspec_kw={"height_ratios": (0.25, 0.75)},
        figsize=figsize,
    )  # creating the 2 subplots
    sns.boxplot(
        data=df, x=feature, ax=ax_box2, showmeans=True, color="violet"
    )  # boxplot will be created and a star will indicate the mean value of the column
    sns.histplot(
        data=df, x=feature, kde=kde, ax=ax_hist2, bins=bins, palette="winter"
    ) if bins else sns.histplot(
        data=df, x=feature, kde=kde, ax=ax_hist2
    )  # For histogram
    ax_hist2.axvline(
        df[feature].mean(), color="green", linestyle="--"
    )  # Add mean to the histogram
    ax_hist2.axvline(
        df[feature].median(), color="black", linestyle="-"
    )  # Add median to the histogram

# function to create labeled barplots


def labeled_barplot(df, feature, perc=False, n=None):
    """
    Barplot with percentage at the top

    data: dataframe
    feature: dataframe column
    perc: whether to display percentages instead of count (default is False)
    n: displays the top n category levels (default is None, i.e., display all levels)
    """

    total = len(df[feature])  # length of the column
    count = df[feature].nunique()
    if n is None:
        plt.figure(figsize=(count + 1, 5))
    else:
        plt.figure(figsize=(n + 1, 5))

    plt.xticks(rotation=90, fontsize=15)
    ax = sns.countplot(
        data=df,
        x=feature,
        palette="Paired",
        order=df[feature].value_counts().index[:n].sort_values(),
    )

    for p in ax.patches:
        if perc == True:
            label = "{:.1f}%".format(
                100 * p.get_height() / total
            )  # percentage of each class of the category
        else:
            label = p.get_height()  # count of each level of the category

        x = p.get_x() + p.get_width() / 2  # width of the plot
        y = p.get_height()  # height of the plot

        ax.annotate(
            label,
            (x, y),
            ha="center",
            va="center",
            size=12,
            xytext=(0, 5),
            textcoords="offset points",
        )  # annotate the percentage

    plt.show()  # show the plot

Univariate Analysis

Prices and Volatility

# Let's look at the current valuations
histogram_boxplot(df, 'Current Price')

histogram_boxplot(df, 'Price Change')

• Most of our ticker valuations are under 200$, with some outliers almost 6 times as much as the rest.
• We seem to have a roughly normal distribution of price changes in the last 13 weeks.
• Prices ranged anywhere between losing 20% to gaining 30% in value.
• Some outliers lost as much our gained as much as 50% in value.

histogram_boxplot(df, 'Volatility')

• Our data here is left skewed, showing that most of our tickers have relatively low volatility.
• The mean is higher than the median, suggesting the outliers are effecting the data here.

ROE

histogram_boxplot(df, 'ROE')

# Filter values in 'ROE' column greater than 600
filtered_df = df[df['ROE'] > 600]

# Display filtered DataFrame
print(filtered_df)

   Ticker Symbol            Security  GICS Sector  \
18          ALLE            Allegion  Industrials   
30           APA  Apache Corporation       Energy   
62           CHK   Chesapeake Energy       Energy   

                     GICS Sub Industry  Current Price  Price Change  \
18                   Building Products      65.919998     13.753230   
30  Oil & Gas Exploration & Production      44.470001     11.397804   
62                Integrated Oil & Gas       4.500000    -38.101788   

    Volatility  ROE  Cash Ratio  Net Cash Flow   Net Income  \
18    1.283795  601          45      -90800000    153900000   
30    2.405408  917          80      698000000 -23528000000   
62    4.559815  687          22    -3283000000 -14685000000   

    Earnings Per Share  Estimated Shares Outstanding  P/E Ratio  P/B Ratio  
18                1.60                    96187500.0  41.199999  -0.877453  
30              -61.20                   384444444.4  93.089287   4.970809  
62              -22.43                   654703522.1  28.407929  -1.840528  

• Similar to our volatility chart, the Return on Equity chart is highly skewed to the left.
• Most of the tickers offered a small return, but some outliers offered a major ROE.
• Three tickers offered an ROE greater than 600: ALLE, APA, and CHK.

Cash Ratio

histogram_boxplot(df, 'Cash Ratio')

Net Cash Flow

histogram_boxplot(df, 'Net Cash Flow')

Net Income

histogram_boxplot(df, 'Net Income')

Earnings Per Share

histogram_boxplot(df, 'Earnings Per Share')

Estimated Shares Outstanding

histogram_boxplot(df, 'Estimated Shares Outstanding')

P/E and P/B Ratios

histogram_boxplot(df, 'P/E Ratio')

histogram_boxplot(df, 'P/B Ratio')

GICS Sector

labeled_barplot(df, 'GICS Sector', perc=True)

labeled_barplot(df, 'GICS Sub Industry', perc=True)

• Industrials represent the highest represtented sector, with Oil & Gas exploration as the highest represented sub sector.

Bivariate Analysis

# correlation check
plt.figure(figsize=(15, 7))
sns.heatmap(
    df.corr(), annot=True, vmin=-1, vmax=1, fmt=".2f", cmap="Spectral"
)
plt.show()

• We have some weak postive correlations between Current price and earnings per share, Net Income and earnings per share, as well as net income and estimated shares outstanding. We also have some weak negative correlation with volatility and net income, price change, and earnings per share. Roe and earnings per share has a negative correlation as well.

Price change analysis

plt.figure(figsize=(8,8))
sns.barplot(data=df, y='GICS Sector', x='Price Change', ci=False)
plt.show()

• Looking at price changes per sector, it's obvious Energy is the worst performing of the group.
• All other sectors rose in price, while Energy dropped considerably and lost value.

Further Sector Analysis

plt.figure(figsize=(8,8))
sns.barplot(data=df, y='GICS Sector', x='Cash Ratio', ci=False)
plt.show()

• All of our sectors show a postive cash ratio.
• Nothing stands out with the Energy sector here compared to the group.
• Telecommunication and Information Technology have the highest amount of Equity against liabilities.

plt.figure(figsize=(8,8))
sns.barplot(data=df, y='GICS Sector', x='P/E Ratio', ci=False)
plt.show()

• Energy hasd by far the highsest P/E Ratio compared to the rest of the group.
• Usually a high P/E ratio means the sector is expected to have a high amount of growth.
• This could be attributed to the recent valuation drop, and could see growth in the future.

plt.figure(figsize=(8,8))
sns.barplot(data=df, y='GICS Sector', x='Volatility', ci=False)
plt.show()

• As suspected, the Volatility in the Energy sector is the highest, where the rest of the group is roughly around the same metric.
• Because of the recent price drop, valuations can jump around quite a bit more than normal for the Energy sector.
• This means investment into this sector can have great returns, but the risk for great losses is equally as high.

sorted_df = df.sort_values(by='Current Price', ascending=False)

plt.figure(figsize=(50,8))
sns.barplot(data=sorted_df, x='Security', y='Current Price', ci=False)
plt.xticks(rotation=90)
plt.show()

• Of all securities listed in our dataset, Priceline.com has the highest valuation in terms of stock price.
• Chesapeake Energy rounds out the bottom as our lowest priced security.

Data Preprocessing

• Duplicate value check
• Missing value treatment
• Outlier check
• Feature engineering (if needed)
• Any other preprocessing steps (if needed)

Outlier Analysis

plt.figure(figsize=(15, 12))

numeric_columns = df.select_dtypes(include=np.number).columns.tolist()

for i, variable in enumerate(numeric_columns):
    plt.subplot(3, 4, i + 1)
    plt.boxplot(df[variable], whis=1.5)
    plt.tight_layout()
    plt.title(variable)

plt.show()

Scaling

# Let's check our numeric columns we will scale and use for clustering
numeric_columns

['Current Price',
 'Price Change',
 'Volatility',
 'ROE',
 'Cash Ratio',
 'Net Cash Flow',
 'Net Income',
 'Earnings Per Share',
 'Estimated Shares Outstanding',
 'P/E Ratio',
 'P/B Ratio']

# Now we can scale our data
scaler = StandardScaler()
subset = df[numeric_columns].copy()
subset_scaled = scaler.fit_transform(subset)

# creating a dataframe of the scaled columns
subset_scaled_df = pd.DataFrame(subset_scaled, columns=subset.columns)

subset_scaled_df.head()

	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio
0	-0.393341	0.493950	0.272749	0.989601	-0.210698	-0.339355	1.554415	1.309399	0.107863	-0.652487	-0.506653
1	-0.220837	0.355439	1.137045	0.937737	0.077269	-0.002335	0.927628	0.056755	1.250274	-0.311769	-0.504205
2	-0.367195	0.602479	-0.427007	-0.192905	-0.033488	0.454058	0.744371	0.024831	1.098021	-0.391502	0.094941
3	0.133567	0.825696	-0.284802	-0.317379	1.218059	-0.152497	-0.219816	-0.230563	-0.091622	0.947148	0.424333
4	-0.260874	-0.492636	0.296470	-0.265515	2.237018	0.133564	-0.202703	-0.374982	1.978399	3.293307	0.199196

K-means Clustering

Elbow Plot Analysis

k_means_df = subset_scaled_df.copy()

# Now we can begin fitting our data and visualize clustering via the elbow plot
clusters = range(1, 15)
meanDistortions = []

for k in clusters:
    model = KMeans(n_clusters=k, random_state=1)
    model.fit(k_means_df)
    prediction = model.predict(k_means_df)
    distortion = (
        sum(np.min(cdist(k_means_df, model.cluster_centers_, "cityblock"), axis=1))
        / k_means_df.shape[0]
    )

    meanDistortions.append(distortion)

    print("Number of Clusters:", k, "\tAverage Distortion:", distortion)

plt.plot(clusters, meanDistortions, "bx-")
plt.xlabel("k")
plt.ylabel("Average Distortion")
plt.title("Selecting k with the Elbow Method", fontsize=20)
plt.show()

Number of Clusters: 1 	Average Distortion: 5.887920700424354
Number of Clusters: 2 	Average Distortion: 5.526545209467102
Number of Clusters: 3 	Average Distortion: 5.2268231521995085
Number of Clusters: 4 	Average Distortion: 5.0429006939190355
Number of Clusters: 5 	Average Distortion: 4.957248320844979
Number of Clusters: 6 	Average Distortion: 4.834180251981078
Number of Clusters: 7 	Average Distortion: 4.717377684716567
Number of Clusters: 8 	Average Distortion: 4.58568591626934
Number of Clusters: 9 	Average Distortion: 4.5221818263791596
Number of Clusters: 10 	Average Distortion: 4.391510667995212
Number of Clusters: 11 	Average Distortion: 4.229491145217527
Number of Clusters: 12 	Average Distortion: 4.211718976799932
Number of Clusters: 13 	Average Distortion: 4.1058985919813775
Number of Clusters: 14 	Average Distortion: 3.993508912391085

# Let's add a bit more structure to our elbow plot
model = KMeans(random_state=1)
visualizer = KElbowVisualizer(model, k=(1, 15), timings=True)
visualizer.fit(k_means_df)
visualizer.show();

• 6 clusters seems to be a good stopping point, although you could argue 7 would work as well. For our purposes we will use 6 clusters.

Silhouette Scores

# Now that we have visualized our elbow plot,  we can compare those results with their silhouette scores
# Let's build an empty data frame for the scores and fill it with results after fitting the models
sil_score = []
cluster_list = range(2, 15)
for n_clusters in cluster_list:
    clusterer = KMeans(n_clusters=n_clusters, random_state=1)
    preds = clusterer.fit_predict((k_means_df))
    score = silhouette_score(k_means_df, preds)
    sil_score.append(score)
    print("For n_clusters = {}, the silhouette score is {})".format(n_clusters, score))

plt.plot(cluster_list, sil_score)
plt.show();

For n_clusters = 2, the silhouette score is 0.43969639509980457)
For n_clusters = 3, the silhouette score is 0.4644405674779404)
For n_clusters = 4, the silhouette score is 0.4577225970476733)
For n_clusters = 5, the silhouette score is 0.43228336443659804)
For n_clusters = 6, the silhouette score is 0.4005422737213617)
For n_clusters = 7, the silhouette score is 0.3976335364987305)
For n_clusters = 8, the silhouette score is 0.40278401969450467)
For n_clusters = 9, the silhouette score is 0.3778585981433699)
For n_clusters = 10, the silhouette score is 0.13458938329968687)
For n_clusters = 11, the silhouette score is 0.1421832155528444)
For n_clusters = 12, the silhouette score is 0.2044669621527429)
For n_clusters = 13, the silhouette score is 0.23424874810104204)
For n_clusters = 14, the silhouette score is 0.12102526472829901)

model = KMeans(random_state=1)
visualizer = KElbowVisualizer(model, k=(2, 15), metric="silhouette", timings=True)
visualizer.fit(k_means_df)
visualizer.show();

# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(4, random_state=1))
visualizer.fit(k_means_df)
visualizer.show();

visualizer = SilhouetteVisualizer(KMeans(7, random_state=1))
visualizer.fit(k_means_df)
visualizer.show();

# let's take 7 as number of clusters
kmeans = KMeans(n_clusters=7, random_state=0)
kmeans.fit(subset_scaled_df)

KMeans(n_clusters=7, random_state=0)

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# creating a copy of the original data
df1 = df.copy()

# adding kmeans cluster labels to the original and scaled dataframes
k_means_df["KM_segments"] = kmeans.labels_
df1["KM_segments"] = kmeans.labels_

df1.head()

	Ticker Symbol	Security	GICS Sector	GICS Sub Industry	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio	KM_segments
0	AAL	American Airlines Group	Industrials	Airlines	42.349998	9.999995	1.687151	135	51	-604000000	7610000000	11.39	6.681299e+08	3.718174	-8.784219	1
1	ABBV	AbbVie	Health Care	Pharmaceuticals	59.240002	8.339433	2.197887	130	77	51000000	5144000000	3.15	1.633016e+09	18.806350	-8.750068	1
2	ABT	Abbott Laboratories	Health Care	Health Care Equipment	44.910000	11.301121	1.273646	21	67	938000000	4423000000	2.94	1.504422e+09	15.275510	-0.394171	1
3	ADBE	Adobe Systems Inc	Information Technology	Application Software	93.940002	13.977195	1.357679	9	180	-240840000	629551000	1.26	4.996437e+08	74.555557	4.199651	5
4	ADI	Analog Devices, Inc.	Information Technology	Semiconductors	55.320000	-1.827858	1.701169	14	272	315120000	696878000	0.31	2.247994e+09	178.451613	1.059810	5

Cluster Profiling

km_cluster_profile = df1.groupby("KM_segments").mean()

km_cluster_profile["count_in_each_segments"] = (
    df1.groupby("KM_segments")["Security"].count().values
)

km_cluster_profile.style.highlight_max(color="lightgreen", axis=0)

	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio	count_in_each_segments
KM_segments
0	48.103077	6.053507	1.163964	27.538462	77.230769	773230769.230769	14114923076.923077	3.958462	3918734987.169230	16.098039	-4.253404	13
1	73.281231	5.002456	1.373721	25.303030	51.018939	5792560.606061	1517540458.333333	3.773201	422805643.026553	23.232765	-3.313539	264
2	26.990000	-14.060688	3.296307	603.000000	57.333333	-585000000.000000	-17555666666.666668	-39.726667	481910081.666667	71.528835	1.638633	3
3	108.304002	10.737770	1.165694	566.200000	26.600000	-278760000.000000	687180000.000000	1.548000	349607057.720000	34.898915	-16.851358	5
4	632.714991	7.374164	1.541343	19.333333	158.333333	-24046333.333333	907393166.666667	16.270000	125797901.323333	123.049240	35.355736	6
5	95.281515	14.717580	1.814754	25.954545	308.909091	645568272.727273	871490181.818182	2.006364	730848546.662727	57.950455	7.992920	22
6	37.282919	-14.529500	2.820301	40.666667	47.555556	-133624777.777778	-1904442925.925926	-4.957037	503635899.112593	86.787432	1.378738	27

for cl in df1["KM_segments"].unique():
    print("In cluster {}, the following companies are present:".format(cl))
    print(df1 [df1["KM_segments"] == cl]["Security"].unique())
    print()

In cluster 1, the following companies are present:
['American Airlines Group' 'AbbVie' 'Abbott Laboratories'
 'Archer-Daniels-Midland Co' 'Ameren Corp' 'American Electric Power'
 'AFLAC Inc' 'American International Group, Inc.'
 'Apartment Investment & Mgmt' 'Assurant Inc' 'Arthur J. Gallagher & Co.'
 'Akamai Technologies Inc' 'Albemarle Corp' 'Alaska Air Group Inc'
 'Allstate Corp' 'Applied Materials Inc' 'AMETEK Inc'
 'Affiliated Managers Group Inc' 'Ameriprise Financial'
 'American Tower Corp A' 'AutoNation Inc' 'Anthem Inc.' 'Aon plc'
 'Amphenol Corp' 'Activision Blizzard' 'AvalonBay Communities, Inc.'
 'American Water Works Company Inc' 'American Express Co' 'Boeing Company'
 'Baxter International Inc.' 'BB&T Corporation' 'Bard (C.R.) Inc.'
 'BIOGEN IDEC Inc.' 'The Bank of New York Mellon Corp.' 'Ball Corp'
 'Bristol-Myers Squibb' 'Boston Scientific' 'BorgWarner'
 'Boston Properties' 'Caterpillar Inc.' 'Chubb Limited' 'CBRE Group'
 'Crown Castle International Corp.' 'Carnival Corp.'
 'CF Industries Holdings Inc' 'Citizens Financial Group' 'Church & Dwight'
 'C. H. Robinson Worldwide' 'CIGNA Corp.' 'Cincinnati Financial'
 'Comerica Inc.' 'CME Group Inc.' 'Cummins Inc.' 'CMS Energy'
 'Centene Corporation' 'CenterPoint Energy' 'Capital One Financial'
 'The Cooper Companies' 'CSX Corp.' 'CenturyLink Inc'
 'Cognizant Technology Solutions' 'Citrix Systems' 'CVS Health'
 'Chevron Corp.' 'Dominion Resources' 'Delta Air Lines' 'Du Pont (E.I.)'
 'Deere & Co.' 'Discover Financial Services' 'Quest Diagnostics'
 'Danaher Corp.' 'The Walt Disney Company' 'Discovery Communications-A'
 'Discovery Communications-C' 'Delphi Automotive' 'Digital Realty Trust'
 'Dun & Bradstreet' 'Dover Corp.' 'Dr Pepper Snapple Group' 'Duke Energy'
 'DaVita Inc.' 'Ecolab Inc.' 'Consolidated Edison' 'Equifax Inc.'
 "Edison Int'l" 'Eastman Chemical' 'Equity Residential'
 'Eversource Energy' 'Essex Property Trust, Inc.' 'E*Trade'
 'Eaton Corporation' 'Entergy Corp.' 'Exelon Corp.' "Expeditors Int'l"
 'Expedia Inc.' 'Extra Space Storage' 'Fastenal Co'
 'Fortune Brands Home & Security' 'FirstEnergy Corp'
 'Fidelity National Information Services' 'Fiserv Inc' 'FLIR Systems'
 'Fluor Corp.' 'Flowserve Corporation' 'FMC Corporation'
 'Federal Realty Investment Trust' 'General Dynamics'
 'General Growth Properties Inc.' 'Corning Inc.' 'General Motors'
 'Genuine Parts' 'Garmin Ltd.' 'Goodyear Tire & Rubber'
 'Grainger (W.W.) Inc.' 'Hasbro Inc.' 'Huntington Bancshares'
 'HCA Holdings' 'Welltower Inc.' 'HCP Inc.' 'Hartford Financial Svc.Gp.'
 'Harley-Davidson' "Honeywell Int'l Inc." 'HP Inc.' 'Hormel Foods Corp.'
 'Henry Schein' 'Host Hotels & Resorts' 'The Hershey Company'
 'Humana Inc.' 'International Business Machines' 'IDEXX Laboratories'
 'Intl Flavors & Fragrances' 'International Paper' 'Interpublic Group'
 'Iron Mountain Incorporated' 'Illinois Tool Works' 'Invesco Ltd.'
 'J. B. Hunt Transport Services' 'Jacobs Engineering Group'
 'Juniper Networks' 'Kimco Realty' 'Kansas City Southern'
 'Leggett & Platt' 'Lennar Corp.' 'Laboratory Corp. of America Holding'
 'LKQ Corporation' 'L-3 Communications Holdings' 'Lilly (Eli) & Co.'
 'Lockheed Martin Corp.' 'Alliant Energy Corp' 'Leucadia National Corp.'
 'Southwest Airlines' 'Level 3 Communications' 'LyondellBasell'
 'Mastercard Inc.' 'Mid-America Apartments' 'Macerich' "Marriott Int'l."
 'Masco Corp.' 'Mattel Inc.' "Moody's Corp" 'Mondelez International'
 'MetLife Inc.' 'Mohawk Industries' 'Mead Johnson' 'McCormick & Co.'
 'Martin Marietta Materials' 'Marsh & McLennan' '3M Company'
 'Altria Group Inc' 'Marathon Petroleum' 'M&T Bank Corp.' 'Mettler Toledo'
 'Mylan N.V.' 'Navient' 'NASDAQ OMX Group' 'NextEra Energy'
 'Nielsen Holdings' 'Norfolk Southern Corp.' 'Northern Trust Corp.'
 'Nucor Corp.' 'Newell Brands' 'Realty Income Corporation' 'Omnicom Group'
 "O'Reilly Automotive" "People's United Financial" 'Pitney-Bowes'
 'PACCAR Inc.' 'PG&E Corp.' 'Public Serv. Enterprise Inc.' 'PepsiCo Inc.'
 'Principal Financial Group' 'Procter & Gamble' 'Progressive Corp.'
 'Pulte Homes Inc.' 'Philip Morris International' 'PNC Financial Services'
 'Pentair Ltd.' 'Pinnacle West Capital' 'PPG Industries' 'PPL Corp.'
 'Prudential Financial' 'Phillips 66' 'Praxair Inc.' 'PayPal'
 'Ryder System' 'Royal Caribbean Cruises Ltd' 'Robert Half International'
 'Roper Industries' 'Republic Services Inc' 'SCANA Corp'
 'Charles Schwab Corporation' 'Sealed Air' 'Sherwin-Williams'
 'SL Green Realty' 'Scripps Networks Interactive Inc.' 'Southern Co.'
 'Simon Property Group Inc' 'Stericycle Inc' 'Sempra Energy'
 'SunTrust Banks' 'State Street Corp.' 'Synchrony Financial'
 'Stryker Corp.' 'Molson Coors Brewing Company' 'Tegna, Inc.'
 'Torchmark Corp.' 'Thermo Fisher Scientific'
 'The Travelers Companies Inc.' 'Tractor Supply Company' 'Tyson Foods'
 'Tesoro Petroleum Co.' 'Total System Services' 'Texas Instruments'
 'Under Armour' 'United Continental Holdings' 'UDR Inc'
 'Universal Health Services, Inc.' 'United Health Group Inc.' 'Unum Group'
 'Union Pacific' 'United Parcel Service' 'United Technologies'
 'Varian Medical Systems' 'Valero Energy' 'Vulcan Materials'
 'Vornado Realty Trust' 'Verisk Analytics' 'Verisign Inc.' 'Ventas Inc'
 'Wec Energy Group Inc' 'Whirlpool Corp.' 'Waste Management Inc.'
 'Western Union Co' 'Weyerhaeuser Corp.' 'Wyndham Worldwide'
 'Xcel Energy Inc' 'XL Capital' 'Dentsply Sirona' 'Xerox Corp.'
 'Xylem Inc.' 'Yum! Brands Inc' 'Zimmer Biomet Holdings' 'Zions Bancorp'
 'Zoetis']

In cluster 5, the following companies are present:
['Adobe Systems Inc' 'Analog Devices, Inc.' 'Alexion Pharmaceuticals'
 'Amgen Inc' 'Broadcom' 'Celgene Corp.' 'eBay Inc.' 'Equinix'
 'Edwards Lifesciences' 'Facebook' 'First Solar Inc'
 'Frontier Communications' 'Halliburton Co.' "McDonald's Corp."
 'Monster Beverage' 'Newmont Mining Corp. (Hldg. Co.)'
 'Skyworks Solutions' 'TripAdvisor' 'Vertex Pharmaceuticals Inc'
 'Waters Corporation' 'Wynn Resorts Ltd' 'Yahoo Inc.']

In cluster 4, the following companies are present:
['Alliance Data Systems' 'Amazon.com Inc' 'Chipotle Mexican Grill'
 'Intuitive Surgical Inc.' 'Priceline.com Inc' 'Regeneron']

In cluster 3, the following companies are present:
['Allegion' 'Charter Communications' 'Colgate-Palmolive' 'Kimberly-Clark'
 'S&P Global, Inc.']

In cluster 2, the following companies are present:
['Apache Corporation' 'Chesapeake Energy' 'Devon Energy Corp.']

In cluster 6, the following companies are present:
['Anadarko Petroleum Corp' 'Arconic Inc' 'Baker Hughes Inc'
 'Cabot Oil & Gas' 'Concho Resources' 'EOG Resources' 'EQT Corporation'
 'Freeport-McMoran Cp & Gld' 'Hess Corporation'
 'Hewlett Packard Enterprise' 'Kinder Morgan' 'The Mosaic Company'
 'Marathon Oil Corp.' 'Murphy Oil' 'Noble Energy Inc' 'Netflix Inc.'
 'Newfield Exploration Co' 'National Oilwell Varco Inc.' 'ONEOK'
 'Occidental Petroleum' 'Quanta Services Inc.' 'Range Resources Corp.'
 'Spectra Energy Corp.' 'Southwestern Energy' 'Teradata Corp.'
 'Williams Cos.' 'Cimarex Energy']

In cluster 0, the following companies are present:
['Bank of America Corp' 'Citigroup Inc.' 'Ford Motor' 'Gilead Sciences'
 'Intel Corp.' 'JPMorgan Chase & Co.' 'Coca Cola Company' 'Merck & Co.'
 'Pfizer Inc.' 'AT&T Inc' 'Verizon Communications' 'Wells Fargo'
 'Exxon Mobil Corp.']

df1.groupby(["KM_segments", "GICS Sector"])['Security'].count()

KM_segments  GICS Sector                
0            Consumer Discretionary          1
             Consumer Staples                1
             Energy                          1
             Financials                      4
             Health Care                     3
             Information Technology          1
             Telecommunications Services     2
1            Consumer Discretionary         32
             Consumer Staples               15
             Energy                          5
             Financials                     44
             Health Care                    29
             Industrials                    50
             Information Technology         20
             Materials                      17
             Real Estate                    26
             Telecommunications Services     2
             Utilities                      24
2            Energy                          3
3            Consumer Discretionary          1
             Consumer Staples                2
             Financials                      1
             Industrials                     1
4            Consumer Discretionary          3
             Health Care                     2
             Information Technology          1
5            Consumer Discretionary          3
             Consumer Staples                1
             Energy                          1
             Health Care                     6
             Information Technology          8
             Materials                       1
             Real Estate                     1
             Telecommunications Services     1
6            Energy                         20
             Industrials                     2
             Information Technology          3
             Materials                       2
Name: Security, dtype: int64

plt.figure(figsize=(20, 20))
plt.suptitle("Boxplot of numerical variables for each cluster")

# selecting numerical columns
num_col = df1.select_dtypes(include=np.number).columns.tolist()

for i, variable in enumerate(num_col):
    plt.subplot(3, 4, i + 1)
    sns.boxplot(data=df1, x="KM_segments", y=variable)

plt.tight_layout(pad=2.0)

Insights

• Group 0 comprises 13 securities, and is a fairly steady set of stocks. Low volatility, minor positive recent price change and average EPS. The only outlier for this group is it has a massive amount of estimated shares outstanding.
• Group 1 is our largest cluster with 264 securities. It has on average a lower volatility. Recent price changes for the group are mostly positive, but lower whisker is negative. That said, it still has the second highest EPS and with the high number of securities, it is a very conservative and diversified group to invest in.
• Group 2 is our biggest red flag and only consists of 3 securities. These have all seen major price decreases lately and are very volatile. While some could argue they are set for a large bounce back, it could also be known as a 'falling knife'. Investors should be extremely cautious with this cluster.
• Group 3 has 5 securities, and we are back to a more average set of financials. This major standout here is a considerably high ROE. These companies are able to provide a much higher value of return compared to investor's equity. With low volatility, this group seems like a steady and safe bet for investments.
• Group 4 has 6 securities, and the lowest estimated shares outstanding. They have rock solid ratios, low volatility, and a high EPS. The only downside is these stocks are by far the most expensive, with only a few other clusters having a couple outliers near its bottom IQR. These are known as 'blue chip' stocks, and highly recommended to invest in.
• Group 5 consists of 22 securities. A very diverse cluster in terms of industry. Volatility is slightly higher here, however, and EPS dips into the negative in the lower IQR. Depending on the level of risk exposure of the investor, I couldn't recommend this group on a broad scale.
• Group 6 consists of 27 securities. This group only consists of 3 industries, most from the energy sector. We've seen earlier that this is the poorest performer and it shows. While not as bad as group 2, I cannot recommend investing here.

Hierarchical Clustering

# Let's create a new dataframe to start our new clustering.
hc_df = subset_scaled_df.copy()

# list of distance metrics
distance_metrics = ["euclidean", "chebyshev", "mahalanobis", "cityblock"]

# list of linkage methods
linkage_methods = ["single", "complete", "average", "weighted"]

high_cophenet_corr = 0
high_dm_lm = [0, 0]

for dm in distance_metrics:
    for lm in linkage_methods:
        Z = linkage(hc_df, metric=dm, method=lm)
        c, coph_dists = cophenet(Z, pdist(hc_df))
        print(
            "Cophenetic correlation for {} distance and {} linkage is {}.".format(
                dm.capitalize(), lm, c
            )
        )
        if high_cophenet_corr < c:
            high_cophenet_corr = c
            high_dm_lm[0] = dm
            high_dm_lm[1] = lm

Cophenetic correlation for Euclidean distance and single linkage is 0.9232271494002922.
Cophenetic correlation for Euclidean distance and complete linkage is 0.7873280186580672.
Cophenetic correlation for Euclidean distance and average linkage is 0.9422540609560814.
Cophenetic correlation for Euclidean distance and weighted linkage is 0.8693784298129404.
Cophenetic correlation for Chebyshev distance and single linkage is 0.9062538164750717.
Cophenetic correlation for Chebyshev distance and complete linkage is 0.598891419111242.
Cophenetic correlation for Chebyshev distance and average linkage is 0.9338265528030499.
Cophenetic correlation for Chebyshev distance and weighted linkage is 0.9127355892367.
Cophenetic correlation for Mahalanobis distance and single linkage is 0.925919553052459.
Cophenetic correlation for Mahalanobis distance and complete linkage is 0.7925307202850002.
Cophenetic correlation for Mahalanobis distance and average linkage is 0.9247324030159736.
Cophenetic correlation for Mahalanobis distance and weighted linkage is 0.8708317490180428.
Cophenetic correlation for Cityblock distance and single linkage is 0.9334186366528574.
Cophenetic correlation for Cityblock distance and complete linkage is 0.7375328863205818.
Cophenetic correlation for Cityblock distance and average linkage is 0.9302145048594667.
Cophenetic correlation for Cityblock distance and weighted linkage is 0.731045513520281.

# Create a print function to give us the highest correlation, distance, and linkage type
print(
    "Highest cophenetic correlation is {}, which is obtained with {} distance and {} linkage.".format(
        high_cophenet_corr, high_dm_lm[0].capitalize(), high_dm_lm[1]
    ))

Highest cophenetic correlation is 0.9422540609560814, which is obtained with Euclidean distance and average linkage.

Euclidean linkages

# list of linkage methods
linkage_methods = ["single", "complete", "average", "centroid", "ward", "weighted"]

high_cophenet_corr = 0
high_dm_lm = [0, 0]

for lm in linkage_methods:
    Z = linkage(hc_df, metric="euclidean", method=lm)
    c, coph_dists = cophenet(Z, pdist(hc_df))
    print("Cophenetic correlation for {} linkage is {}.".format(lm, c))
    if high_cophenet_corr < c:
        high_cophenet_corr = c
        high_dm_lm[0] = "euclidean"
        high_dm_lm[1] = lm

Cophenetic correlation for single linkage is 0.9232271494002922.
Cophenetic correlation for complete linkage is 0.7873280186580672.
Cophenetic correlation for average linkage is 0.9422540609560814.
Cophenetic correlation for centroid linkage is 0.9314012446828154.
Cophenetic correlation for ward linkage is 0.7101180299865353.
Cophenetic correlation for weighted linkage is 0.8693784298129404.

print(
    "Highest cophenetic correlation is {}, which is obtained with {} linkage.".format(
        high_cophenet_corr, high_dm_lm[1]
    )
)

Highest cophenetic correlation is 0.9422540609560814, which is obtained with average linkage.

• Euclidean distance offered the highest cophenetic scores with the average linkage.

Dendrograms

# list of linkage methods
linkage_methods = ["single", "complete", "average", "centroid", "ward", "weighted"]

# lists to save results of cophenetic correlation calculation
compare_cols = ["Linkage", "Cophenetic Coefficient"]
compare = []

# to create a subplot image
fig, axs = plt.subplots(len(linkage_methods), 1, figsize=(15, 30))

# We will enumerate through the list of linkage methods above
# For each linkage method, we will plot the dendrogram and calculate the cophenetic correlation
for i, method in enumerate(linkage_methods):
    Z = linkage(hc_df, metric="euclidean", method=method)

    dendrogram(Z, ax=axs[i])
    axs[i].set_title(f"Dendrogram ({method.capitalize()} Linkage)")

    coph_corr, coph_dist = cophenet(Z, pdist(hc_df))
    axs[i].annotate(
        f"Cophenetic\nCorrelation\n{coph_corr:0.2f}",
        (0.80, 0.80),
        xycoords="axes fraction",
    )

    compare.append([method, coph_corr])

# create and print a dataframe to compare cophenetic correlations for different linkage methods
df_cc = pd.DataFrame(compare, columns=compare_cols)
df_cc = df_cc.sort_values(by="Cophenetic Coefficient", ascending=False)
df_cc

	Linkage	Cophenetic Coefficient
2	average	0.942254
3	centroid	0.931401
0	single	0.923227
5	weighted	0.869378
1	complete	0.787328
4	ward	0.710118

HCmodel = AgglomerativeClustering(n_clusters=8, affinity="euclidean", linkage="average")
HCmodel.fit(hc_df)

AgglomerativeClustering(affinity='euclidean', linkage='average', n_clusters=8)

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# creating a copy of the original data
df2 = df.copy()

# adding hierarchical cluster labels to the original and scaled dataframes
hc_df["HC_segments"] = HCmodel.labels_
df2["HC_segments"] = HCmodel.labels_

hc_cluster_profile = df2.groupby("HC_segments").mean()

hc_cluster_profile["count_in_each_segments"] = (
    df2.groupby("HC_segments")["Security"].count().values
)

hc_cluster_profile.style.highlight_max(color="lightgreen", axis=0)

	Current Price	Price Change	Volatility	ROE	Cash Ratio	Net Cash Flow	Net Income	Earnings Per Share	Estimated Shares Outstanding	P/E Ratio	P/B Ratio	count_in_each_segments
HC_segments
0	327.006671	21.917380	2.029752	4.000000	106.000000	698240666.666667	287547000.000000	0.750000	366763235.300000	400.989188	-5.322376	3
1	25.640000	11.237908	1.322355	12.500000	130.500000	16755500000.000000	13654000000.000000	3.295000	2791829362.100000	13.649696	1.508484	2
2	75.017416	3.937751	1.513415	35.621212	66.545455	-39846757.575758	1549443100.000000	2.904682	562266326.402576	29.091275	-2.146308	330
3	104.660004	16.224320	1.320606	8.000000	958.000000	592000000.000000	3669000000.000000	1.310000	2800763359.000000	79.893133	5.884467	1
4	1274.949951	3.190527	1.268340	29.000000	184.000000	-1671386000.000000	2551360000.000000	50.090000	50935516.070000	25.453183	-1.052429	1
5	276.570007	6.189286	1.116976	30.000000	25.000000	90885000.000000	596541000.000000	8.910000	66951851.850000	31.040405	129.064585	1
6	4.500000	-38.101788	4.559815	687.000000	22.000000	-3283000000.000000	-14685000000.000000	-22.430000	654703522.100000	28.407929	-1.840528	1
7	44.470001	11.397804	2.405408	917.000000	80.000000	698000000.000000	-23528000000.000000	-61.200000	384444444.400000	93.089287	4.970809	1

for cl in df2["HC_segments"].unique():
    print("In cluster {}, the following companies are present:".format(cl))
    print(df2 [df2["HC_segments"] == cl]["Security"].unique())
    print()

In cluster 2, the following companies are present:
['American Airlines Group' 'AbbVie' 'Abbott Laboratories'
 'Adobe Systems Inc' 'Analog Devices, Inc.' 'Archer-Daniels-Midland Co'
 'Ameren Corp' 'American Electric Power' 'AFLAC Inc'
 'American International Group, Inc.' 'Apartment Investment & Mgmt'
 'Assurant Inc' 'Arthur J. Gallagher & Co.' 'Akamai Technologies Inc'
 'Albemarle Corp' 'Alaska Air Group Inc' 'Allstate Corp' 'Allegion'
 'Applied Materials Inc' 'AMETEK Inc' 'Affiliated Managers Group Inc'
 'Amgen Inc' 'Ameriprise Financial' 'American Tower Corp A'
 'AutoNation Inc' 'Anthem Inc.' 'Aon plc' 'Anadarko Petroleum Corp'
 'Amphenol Corp' 'Arconic Inc' 'Activision Blizzard'
 'AvalonBay Communities, Inc.' 'Broadcom'
 'American Water Works Company Inc' 'American Express Co' 'Boeing Company'
 'Baxter International Inc.' 'BB&T Corporation' 'Bard (C.R.) Inc.'
 'Baker Hughes Inc' 'BIOGEN IDEC Inc.' 'The Bank of New York Mellon Corp.'
 'Ball Corp' 'Bristol-Myers Squibb' 'Boston Scientific' 'BorgWarner'
 'Boston Properties' 'Citigroup Inc.' 'Caterpillar Inc.' 'Chubb Limited'
 'CBRE Group' 'Crown Castle International Corp.' 'Carnival Corp.'
 'Celgene Corp.' 'CF Industries Holdings Inc' 'Citizens Financial Group'
 'Church & Dwight' 'C. H. Robinson Worldwide' 'Charter Communications'
 'CIGNA Corp.' 'Cincinnati Financial' 'Colgate-Palmolive' 'Comerica Inc.'
 'CME Group Inc.' 'Chipotle Mexican Grill' 'Cummins Inc.' 'CMS Energy'
 'Centene Corporation' 'CenterPoint Energy' 'Capital One Financial'
 'Cabot Oil & Gas' 'The Cooper Companies' 'CSX Corp.' 'CenturyLink Inc'
 'Cognizant Technology Solutions' 'Citrix Systems' 'CVS Health'
 'Chevron Corp.' 'Concho Resources' 'Dominion Resources' 'Delta Air Lines'
 'Du Pont (E.I.)' 'Deere & Co.' 'Discover Financial Services'
 'Quest Diagnostics' 'Danaher Corp.' 'The Walt Disney Company'
 'Discovery Communications-A' 'Discovery Communications-C'
 'Delphi Automotive' 'Digital Realty Trust' 'Dun & Bradstreet'
 'Dover Corp.' 'Dr Pepper Snapple Group' 'Duke Energy' 'DaVita Inc.'
 'Devon Energy Corp.' 'eBay Inc.' 'Ecolab Inc.' 'Consolidated Edison'
 'Equifax Inc.' "Edison Int'l" 'Eastman Chemical' 'EOG Resources'
 'Equinix' 'Equity Residential' 'EQT Corporation' 'Eversource Energy'
 'Essex Property Trust, Inc.' 'E*Trade' 'Eaton Corporation'
 'Entergy Corp.' 'Edwards Lifesciences' 'Exelon Corp.' "Expeditors Int'l"
 'Expedia Inc.' 'Extra Space Storage' 'Ford Motor' 'Fastenal Co'
 'Fortune Brands Home & Security' 'Freeport-McMoran Cp & Gld'
 'FirstEnergy Corp' 'Fidelity National Information Services' 'Fiserv Inc'
 'FLIR Systems' 'Fluor Corp.' 'Flowserve Corporation' 'FMC Corporation'
 'Federal Realty Investment Trust' 'First Solar Inc'
 'Frontier Communications' 'General Dynamics'
 'General Growth Properties Inc.' 'Gilead Sciences' 'Corning Inc.'
 'General Motors' 'Genuine Parts' 'Garmin Ltd.' 'Goodyear Tire & Rubber'
 'Grainger (W.W.) Inc.' 'Halliburton Co.' 'Hasbro Inc.'
 'Huntington Bancshares' 'HCA Holdings' 'Welltower Inc.' 'HCP Inc.'
 'Hess Corporation' 'Hartford Financial Svc.Gp.' 'Harley-Davidson'
 "Honeywell Int'l Inc." 'Hewlett Packard Enterprise' 'HP Inc.'
 'Hormel Foods Corp.' 'Henry Schein' 'Host Hotels & Resorts'
 'The Hershey Company' 'Humana Inc.' 'International Business Machines'
 'IDEXX Laboratories' 'Intl Flavors & Fragrances' 'International Paper'
 'Interpublic Group' 'Iron Mountain Incorporated'
 'Intuitive Surgical Inc.' 'Illinois Tool Works' 'Invesco Ltd.'
 'J. B. Hunt Transport Services' 'Jacobs Engineering Group'
 'Juniper Networks' 'JPMorgan Chase & Co.' 'Kimco Realty' 'Kimberly-Clark'
 'Kinder Morgan' 'Coca Cola Company' 'Kansas City Southern'
 'Leggett & Platt' 'Lennar Corp.' 'Laboratory Corp. of America Holding'
 'LKQ Corporation' 'L-3 Communications Holdings' 'Lilly (Eli) & Co.'
 'Lockheed Martin Corp.' 'Alliant Energy Corp' 'Leucadia National Corp.'
 'Southwest Airlines' 'Level 3 Communications' 'LyondellBasell'
 'Mastercard Inc.' 'Mid-America Apartments' 'Macerich' "Marriott Int'l."
 'Masco Corp.' 'Mattel Inc.' "McDonald's Corp." "Moody's Corp"
 'Mondelez International' 'MetLife Inc.' 'Mohawk Industries'
 'Mead Johnson' 'McCormick & Co.' 'Martin Marietta Materials'
 'Marsh & McLennan' '3M Company' 'Monster Beverage' 'Altria Group Inc'
 'The Mosaic Company' 'Marathon Petroleum' 'Merck & Co.'
 'Marathon Oil Corp.' 'M&T Bank Corp.' 'Mettler Toledo' 'Murphy Oil'
 'Mylan N.V.' 'Navient' 'Noble Energy Inc' 'NASDAQ OMX Group'
 'NextEra Energy' 'Newmont Mining Corp. (Hldg. Co.)'
 'Newfield Exploration Co' 'Nielsen Holdings'
 'National Oilwell Varco Inc.' 'Norfolk Southern Corp.'
 'Northern Trust Corp.' 'Nucor Corp.' 'Newell Brands'
 'Realty Income Corporation' 'ONEOK' 'Omnicom Group' "O'Reilly Automotive"
 'Occidental Petroleum' "People's United Financial" 'Pitney-Bowes'
 'PACCAR Inc.' 'PG&E Corp.' 'Public Serv. Enterprise Inc.' 'PepsiCo Inc.'
 'Pfizer Inc.' 'Principal Financial Group' 'Procter & Gamble'
 'Progressive Corp.' 'Pulte Homes Inc.' 'Philip Morris International'
 'PNC Financial Services' 'Pentair Ltd.' 'Pinnacle West Capital'
 'PPG Industries' 'PPL Corp.' 'Prudential Financial' 'Phillips 66'
 'Quanta Services Inc.' 'Praxair Inc.' 'PayPal' 'Ryder System'
 'Royal Caribbean Cruises Ltd' 'Regeneron' 'Robert Half International'
 'Roper Industries' 'Range Resources Corp.' 'Republic Services Inc'
 'SCANA Corp' 'Charles Schwab Corporation' 'Spectra Energy Corp.'
 'Sealed Air' 'Sherwin-Williams' 'SL Green Realty'
 'Scripps Networks Interactive Inc.' 'Southern Co.'
 'Simon Property Group Inc' 'S&P Global, Inc.' 'Stericycle Inc'
 'Sempra Energy' 'SunTrust Banks' 'State Street Corp.'
 'Skyworks Solutions' 'Southwestern Energy' 'Synchrony Financial'
 'Stryker Corp.' 'AT&T Inc' 'Molson Coors Brewing Company'
 'Teradata Corp.' 'Tegna, Inc.' 'Torchmark Corp.'
 'Thermo Fisher Scientific' 'TripAdvisor' 'The Travelers Companies Inc.'
 'Tractor Supply Company' 'Tyson Foods' 'Tesoro Petroleum Co.'
 'Total System Services' 'Texas Instruments' 'Under Armour'
 'United Continental Holdings' 'UDR Inc' 'Universal Health Services, Inc.'
 'United Health Group Inc.' 'Unum Group' 'Union Pacific'
 'United Parcel Service' 'United Technologies' 'Varian Medical Systems'
 'Valero Energy' 'Vulcan Materials' 'Vornado Realty Trust'
 'Verisk Analytics' 'Verisign Inc.' 'Vertex Pharmaceuticals Inc'
 'Ventas Inc' 'Verizon Communications' 'Waters Corporation'
 'Wec Energy Group Inc' 'Wells Fargo' 'Whirlpool Corp.'
 'Waste Management Inc.' 'Williams Cos.' 'Western Union Co'
 'Weyerhaeuser Corp.' 'Wyndham Worldwide' 'Wynn Resorts Ltd'
 'Cimarex Energy' 'Xcel Energy Inc' 'XL Capital' 'Exxon Mobil Corp.'
 'Dentsply Sirona' 'Xerox Corp.' 'Xylem Inc.' 'Yahoo Inc.'
 'Yum! Brands Inc' 'Zimmer Biomet Holdings' 'Zions Bancorp' 'Zoetis']

In cluster 5, the following companies are present:
['Alliance Data Systems']

In cluster 0, the following companies are present:
['Alexion Pharmaceuticals' 'Amazon.com Inc' 'Netflix Inc.']

In cluster 7, the following companies are present:
['Apache Corporation']

In cluster 1, the following companies are present:
['Bank of America Corp' 'Intel Corp.']

In cluster 6, the following companies are present:
['Chesapeake Energy']

In cluster 3, the following companies are present:
['Facebook']

In cluster 4, the following companies are present:
['Priceline.com Inc']

df2.groupby(["HC_segments", "GICS Sector"])['Security'].count()

HC_segments  GICS Sector                
0            Consumer Discretionary          1
             Health Care                     1
             Information Technology          1
1            Financials                      1
             Information Technology          1
2            Consumer Discretionary         38
             Consumer Staples               19
             Energy                         28
             Financials                     48
             Health Care                    39
             Industrials                    53
             Information Technology         29
             Materials                      20
             Real Estate                    27
             Telecommunications Services     5
             Utilities                      24
3            Information Technology          1
4            Consumer Discretionary          1
5            Information Technology          1
6            Energy                          1
7            Energy                          1
Name: Security, dtype: int64

• Compared to our K-means clustering, the hierarchical clustering did a poor job at grouping everything together.

K-means vs Hierarchical Clustering

You compare several things, like:

• Which clustering technique took less time for execution?

• K-means was much faster in this scenario.

• Which clustering technique gave you more distinct clusters, or are they the same?

• K-means was far superior at giving distinct clusters. Perhaps if outliers were treated our results may have been different, but by leaving them in there is no comparison between the two as far as performace.

• How many observations are there in the similar clusters of both algorithms?

• Both algorithims chose one cluster that was significantly larger than the others.

• How many clusters are obtained as the appropriate number of clusters from both algorithms?

• Between 6-8 clusters seemed appropriate given the treatment of the data for both algos.

Actionable Insights and Recommendations

• K-means gave us a great set of clusters to use for different types of investors.
• Cluster 4 is our strongest set of securities, or 'blue chips'. Investment into these stocks are highly recommended for steady growth.
• Clusters 0, 1 and 3 are recommended for slower, more conservative investors. Cluster 1 especially as it is the most diverse of all and would have the lowest amount of risk.
• Clusters 2 and 6 should be avoided as investments. These clusters represent securities that have recently performed poorly and have higher volatility.
• Cluster 5 is the last to be considered for investment, but only for experienced investors who don't mind a biut more exposure to risk. While a diverse group, it shows a greater risk/reward ratio compared to the rest of the group.
• Any further insight from specific clusters can be found in the insights section of the K-means clustering.